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Full text of "Men Of Mathematics"

MEN OF MATHEMATICS
Boole was thirty-nine when this appeared. It is somewhat
unusual for a mathematician as old as that to produce work of
such profound originality, but the phenomenon is accounted
for when we remember the long, devious path Boole was com-
pelled to follow before he could set his face fairly toward his
goal. (Compare the careers of Boole and Weierstrass.)
A few extracts will give some idea of Boole's style and the
scope of his work.
'The design of the following treatise is to investigate the
fundamental laws of those operations of the mind by which
reasoning is performed; to give expression to them in the lan-
guage of a Calculus, and upon this foundation to establish the
science of Logic and construct its method; to make that method
itself the basis of a general method for the application of the
mathematical doctrine of probabilities; and, finall}-, to collect
from the various elements of truth brought to view in the course
of these inquiries some probable intimations concerning the
nature and constitution of the human mind. ...'
'Shall we then err in regarding that as the true science of
Logic which, laying down certain elementary laws, confirmed
by the very testimony of the mind, permits us thence to deduce,
by uniform processes, the entire chain of its secondary conse-
quences, and furnishes, for its practical applications, methods
of perfect generality? .. /
4There exist, indeed, certain general principles founded in the
very nature of language, by which the use of symbols, which are
but the elements of scientific language, is determined. To a
certain extent these elements are arbitrary. Their interpretation
is purely conventional: we are permitted to employ them in
whatever sense we please. But this permission is limited by two
indispensable conditions, - first, that from the sense once con-
\rentionally established we never, in the same process of reason-
ing, depart; secondly, that the laws by which the process is
conducted be founded exclusively upon the above fixed sense
or meaning of the symbols employed. In accordance with these
principles, any agreement which may be established between
the laws of the symbols of Logic and those of Algebra can but
issue in an agreement of processes. The two provinces of inter-
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